Question
Consider the following multiple sequence alignment of four DNA sequences. $\begin{matrix}A & C & T & A \\ A & C & T & G \\ A & G & T & C \\ A & G & C & T \end{matrix} $ Shannon's entropy of the above alignment is ________.
To compute Shannon's entropy for the given DNA sequence alignment, we follow these steps:
- Collect Column Frequencies: Each column in the alignment needs to be analyzed to find the frequency of each nucleotide (A, C, G, T). For instance:
| Position | Nucleotides | Frequencies |
|---|---|---|
| 1 | A, A, A, A | A=4/4 |
| 2 | C, C, G, G | C=2/4, G=2/4 |
| 3 | T, T, T, C | T=3/4, C=1/4 |
| 4 | A, G, C, T | A=1/4, G=1/4, C=1/4, T=1/4 |
- Compute Shannon's Entropy for Each Column: The formula for Shannon's entropy \(H\) for a column is \(-\sum (p_i \cdot \log_2(p_i))\), where \(p_i\) is the frequency of nucleotide \(i\) in that column.
- Column 1: \(- (1 \cdot \log_2(1)) = 0\)
- Column 2: \(- (0.5 \cdot \log_2(0.5) + 0.5 \cdot \log_2(0.5)) = 1\)
- Column 3: \(- (0.75 \cdot \log_2(0.75) + 0.25 \cdot \log_2(0.25)) = 0.81\)
- Column 4: \(- (0.25 \cdot \log_2(0.25) + 0.25 \cdot \log_2(0.25) + 0.25 \cdot \log_2(0.25) + 0.25 \cdot \log_2(0.25)) = 2\)
- Calculate Total Entropy: The total entropy \(H_{total}\) is the sum of the individual entropies: \(H_{total} = 0 + 1 + 0.81 + 2 = 3.81\)
The computed Shannon's entropy is 3.81, which falls within the expected range of 3.8 to 3.82.
Was this answer helpful?
Important Questions from Molecular Structure of Genes and Chromosomes
- All pseudogenes DO NOT code for a __________.
- C-value paradox refers to
The transcription factor X binds a 10 base pair DNA stretch. In the DNA of an organism, X was found to bind at 20 distinct sites. An analysis of these 20 binding sites showed the following distribution:
Base Position in the binding site 1 2 3 4 5 6 7 8 9 10 A 11 0 0 0 16 2 4 0 4 3 T 3 0 19 0 1 3 4 20 2 4 G 4 20 0 0 2 4 6 0 12 2 C 2 0 1 20 1 11 6 0 2 11 What is the consensus sequence for the binding site of X?
- Which of the following statements are CORRECT when a protein sequence database is searched using the BLAST algorithm?
P. A larger E-value indicates higher sequence similarity
Q. E-value < $10^{-10}$ indicates sequence homology
R. A higher BLAST score indicates higher sequence similarity
S. E-value > $10^{10}$ indicates sequence homology - Which one of the following DNA sequences carries an invert repeat?
Need Expert Advice?
